Positron emission tomography (PET) is a branch of nuclear medicine in which a positron-emitting radiopharmaceutical is introduced into the body of a patient. As the radiopharmaceutical decays, positrons are generated. More specifically, each of a plurality of positrons reacts with an electron in what is known as a positron annihilation event, thereby generating a coincident pair of gamma photons which travel substantially in opposite directions along a line of coincidence. A gamma photon pair detected within a coincidence time is ordinarily recorded by the PET scanner as an annihilation event.
In time-of-flight (“TOF”) imaging, the time within the coincidence interval at which each gamma photon in the coincident pair is detected is also measured. The time-of-flight information provides an indication of the annihilation location of the detected event along the line of coincidence. Data from a plurality of annihilation events is used to reconstruct or create images of the patient or object scanned, typically by using statistical (iterative) or analytical reconstruction algorithms.
FIG. 1 illustrates the transaxial and axial coordinates of an emitted positron and the measured line of response (LOR) of a 3D detector. The coordinates (xe, ye, ze) or (se, te, ze) define the emitted positron's image coordinate. The measured LOR's projection coordinate can be defined by either (s, φ, z, θ), where z=(za+zb)/2, or may include the additional dimension t for a TOF-LOR.
In PET, random coincidences occur due to the finite width of the coincidence window, which is used to detect true coincidences. If two uncorrelated single events are detected within the coincidence window, they can mistakenly be identified as a true coincidence event and recorded. The rate of random events is proportional to the single event rate on each detector and the size of coincidence window, as shown in Equation (1):Cij=2τrirj  (1)in which Cij represents the random coincidences count rate on the LOR that connects the i-th and j-th detectors, rirj represents the single count event rates of the i-th and j-th detectors, and τ is the coincidence window size.
Random coincidences can comprise a large portion of the recorded prompt coincidence events (which include true, scatter, and random coincidence events), especially in the operation of a 3D PET scanner and high radioactivity concentration. If not compensated for properly, random coincidence events can introduce substantial quantitative errors in the reconstructed images.
The amount of random events in prompt coincidence events is determined by the coincidence timing window and the single event count-rate of two opposing crystals that detect the coincidence. The coincidence timing window is set by the size of the acquisition field-of-view (FOV) and the timing resolution of the scanner. The typical FOV for a PET scanner is a three-dimensional cylinder, with a centered circular region in the transverse plane and the same axial length as the scanner. Therefore, by default, the acquisition FOV refers to the diameter of the circular region in the transverse plane. For PET whole-body imaging, the FOV is usually 576 mm to 700 mm. The timing resolution depends on the type of crystal, optical photon detector, and front-end electronics of the data acquisition system. For LYSO crystals, the typical timing resolution is 500 ps to 650 ps. The related coincidence timing window is then 4 ns to 6 ns for whole-body imaging. The random fraction (random/prompt) in FDG whole-body applications is about 30% to 50%, depending on the activity concentration of the axial section of the patient.
However, the fixed coincidence window method inevitably introduces a large amount of random events in the prompt coincidence data. For example, for a fixed phantom/patient with the same single event count-rate over all crystals, the total amount of randoms is directly proportional to the circular area of the acquisition FOV and the coincidence window FOV size. Note that the coincidence window FOV can be computed as 2*150 (mm 1 ns)*coinWin (ns), in which coinWin is the coincidence window length in ns.
Various methods have been proposed to reduce the number of random events.
In one approach, a truncated time window smaller than the maximum time coincidence window of the PET scanner is used to restrict projection data acquisition to only a central subset of TOF bins that is less than all available TOF bins. The truncated time-window FOV can represent a region of interest of an object being imaged that is smaller than the actual object. It can also lower the list-mode data transfer rate, e.g., for a high-count-rate Rb-82 PET cardiac imaging application. This truncated time window method not only reduces the number of random events, but also reduces the number of true events, if the truncated time window is set too aggressively.
In another approach, an individual patient's CT morphological information is used to tailor the time coincidence window. For a particular line-of-response (LOR), the lower- and upper-bound of the TOF bins are determined by finding the entrance and exit points of the LOR that intersects with the patient's body. The effect of the TOF masking is a trimming of the sinogram along the boundary of the patient, eliminating events outside the patient that are mainly random. However, since the statistical uncertainty of timing (i.e., the timing resolution is not perfect) is not taken into consideration, about 10-15% of true coincidences are also rejected in this TOF masking approach.
In a third approach, a variable coincidence window as a function of different ring differences is used to reduce random events. This method is more applicable for long axial-FOV PET scanners, e.g., those having greater than a 20-cm axial FOV.
Other random reduction methods include using an adjustable coincidence window between different pairs of detector modules, and/or using sinogram radial bin locations to reject LORs that are located outside the FOV. These methods do not take timing resolution into consideration, and thus will inevitable also reduce true coincidence events.